Necessary and Sufficient Conditions for the Existence of Positive Solution for Singular Boundary Value Problems on Time Scales. (13th October 2009)

• Record Type: Journal Article
• Authors: Feng, Meiqiang; Zhang, Xuemei; Li, Xianggui; Ge, Weigao
• Other Names: Cabada Alberto Academic Editor.
• Is Part Of: Advances in difference equations. Volume 2009(2009)
• Publication Date: 2009-10-13
• Subjects: Difference equations -- Periodicals; 515.625
• DOI: 10.1155/2009/737461
• Languages: English
• ISSNs: 1687-1847

Abstract

Abstract : By constructing available upper and lower solutions and combining the Schauder's fixed point theorem with maximum principle, this paper establishes sufficient and necessary conditions to guarantee the existence ofC l d [ 0, 1 ] 𝕋 as well asC l d Δ [ 0, 1 ] 𝕋 positive solutions for a class of singular boundary value problems on time scales. The results significantly extend and improve many known results for both the continuous case and more general time scales. We illustrate our results by one example.